Bayesian Approach for Estimating Biological Treatment Parameters under Flooding Condition

Abstract

Wastewater treatment plants (WWTPs) have a significant role in urban system serviceability. Flooding can impact the performance of WWTPs by causing malfunction in its unit operations, which results in releasing partially treated or even untreated effluent into natural water bodies, causing environmental predicaments of significant proportions. In particular, the biological parameters could go through changes that need to be assessed and monitored in order to implement effective adaptation strategies. In this study, the uncertainty analysis and estimation of biological parameters of WWTP modeling under flood conditions is investigated by using Bayesian inference. In the first step, the proper prior distribution is fitted to the important parameters recognized by sensitivity analysis. Next, the effluent parameters in times of wet weather [five-day biochemical oxygen demand (BOD5), total suspended solids (TSS), and ammonia and total nitrogen (TN)] are used as new data to update and estimate the value of the parameters. By using the Bayesian inference concept, the posterior distributions of parameters are obtained. Two types of likelihood functions are used: formal, derived from the stochastic error series, and informal, which uses predefined performance criteria to characterize the relationship between the observation and model output. Finally, Markov chain Monte Carlo (MCMC) methods are used to sample from the posterior distribution. Parameter posteriors are summarized using the posterior mean for parameter estimation (in wet weather) and coefficient of variation (CV) for degree of uncertainty. The results show that there are a number of parameters for which the value of CV drops significantly at the time of flood conditions. This means their uncertainty decreases, whereas for some other parameters, it is negligible. Moreover, by using the formal likelihood function, the parameters are pinpointed more precisely, and the range of parameters is narrowed up to 98%. The methodology developed in this study could be used to plan for effective simulation and monitoring of WWTPs in different geographic settings.